Big Red

Big Red was an insane lumberjack briefly encountered by Max in a deserted shack, known as Lockjaw. For unknown reasons, Big Red was locked inside of a wooden crate, and upon bursting out of it came after Max with an axe. Max was able to lock him back up inside the crate however.

"Big Red" was probably just a taunting nickname Max came up for the maniac based on the blood-red coloration of his skin, whose proper name was Lockjaw.